{
  "$schema": "../../../schemas/mko-v0.4.schema.json",
  "schema_version": "mko-v0.4",
  "id": "mko-diagnostic-mathematical-assessment",
  "semantic_family_id": "sf-diagnostic-mathematical-assessment",
  "type": "concept",
  "version": "0.10.0",
  "language": "zh-Hant",
  "titles": {
    "zh-Hant": "診斷性數學評量記錄"
  },
  "summary": {
    "zh-Hant": "診斷性數學評量記錄把題目、期望、作答與明示判定規則綁在一起，只產生可追溯的規則符合狀態。"
  },
  "statement": {
    "zh-Hant": "本條目把診斷記錄定義為題目身分、期望數學結果、觀察到的合成作答與判定規則。規則可標記作答是否符合期望，但單一反應不能推論真實學生的能力、原因、人格或學習成效。"
  },
  "formula": {
    "tex": "D(q,r)",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>D</mi><mo>(</mo><mi>q</mi><mo>,</mo><mi>r</mi><mo>)</mo></mrow></math>",
    "semantic_ast": {
      "type": "function_call",
      "callee": {
        "type": "symbol",
        "name": "D",
        "glyph": "D"
      },
      "arguments": [
        {
          "type": "symbol",
          "name": "q",
          "glyph": "q"
        },
        {
          "type": "symbol",
          "name": "r",
          "glyph": "r"
        }
      ]
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.4.0",
      "source_sha256": "f84bdb6532337632abc9e45b073b6081a0182cedc4413b863bb8ae04c5e9c84e"
    }
  },
  "assumptions": [
    {
      "id": "a1",
      "zh-Hant": "題庫全部使用合成作答資料，不含真實學習者、個資或行為紀錄。"
    },
    {
      "id": "a2",
      "zh-Hant": "判定碼只描述明示數學規則是否相符，不把錯誤結果心理化或因果化。"
    }
  ],
  "symbols": [
    {
      "token": "D",
      "role": "diagnostic_record",
      "role_zh": "規則式診斷記錄",
      "scope": "representative_formula"
    },
    {
      "token": "q",
      "role": "item_record",
      "role_zh": "題目與期望",
      "scope": "representative_formula"
    },
    {
      "token": "r",
      "role": "synthetic_response",
      "role_zh": "合成作答",
      "scope": "representative_formula"
    }
  ],
  "dependencies": [
    {
      "id": "mko-proposition",
      "title_zh": "命題",
      "reason_zh": "期望與判定可寫成真假命題。"
    },
    {
      "id": "mko-counterexample",
      "title_zh": "反例",
      "reason_zh": "反例可否定普遍主張，但不診斷人的特質。"
    },
    {
      "id": "mko-mathematical-representation",
      "title_zh": "數學表徵",
      "reason_zh": "作答與期望需在相同表示與解讀規則下比較。"
    }
  ],
  "explanation": {
    "paragraphs_zh": [
      "一份可重播記錄要保留題目、期望、作答與規則；缺欄時只能標記紀錄不完整。",
      "整數和、分數等價與代入值可用精確運算重算，判定碼只分為符合或不符合規則期望。",
      "多題證據、教學歷程與有效測量模型才可能支援更廣的教育推論，本輪不建立這些主張。"
    ],
    "common_misconception_zh": "看到單題錯誤就宣稱學習障礙、概念缺失或教學無效。"
  },
  "proofs": [],
  "computational_companions": [],
  "verification": {
    "computational_status": "not_evaluated_no_computational_claim",
    "warning_zh": "合成規則分類不是對真實學生的診斷，也不是學習效果證據。",
    "evidence_refs": [],
    "producers": [
      {
        "id": "lean-mathlib",
        "adapter": "formal_system",
        "config_path": "formal/lean/lakefile.toml",
        "status": "configured"
      }
    ]
  },
  "formalization": {
    "status": "not_formalized",
    "target_systems": [
      "Lean 4",
      "Mathlib"
    ],
    "next_obligation_zh": "加入多題量尺、效度、信度、人工覆核與隱私治理，但保持與單題規則記錄分層。"
  },
  "provenance": {
    "origin": "ocme_local_ai_materialization_candidate",
    "note_zh": "依 research/atlas-diagnostic-mathematical-assessment.md 整理；2026-10-13 脈衝 R02（使用者手動接續 2026-10-21 工作序列；實際日期仍為 2026-10-13），英文及 Lean 依使用者指示延後。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-10-13"
  }
}